What year did Grover Cleveland accept the Statue of Liberty?

Yes, when the Statue of Liberty was formally dedicated on October 28, 1886, Grover Cleveland was the President of The United States of America. It was determined that the United States would accept the Statue of Liberty on March 3, 1877. This was President Ulysses S. Grant's final day in office, President Grant signed a joint resolution that authorized the President to accept the statue when it was presented by France and to select a site for it. One of what would eventually become one of the Statue of Liberty's arms was displayed in New York City, in Madison Square Park, from 1876 to 1882. That time period (1876 to 1882) saw the presidencies of Ulysses S. Grant, Rutherford Hayes, James Garfield, Chester Arthur and Grover Cleveland in that order. Hope this answers your question.